Hybrid spin Hall nano-oscillators based on ferromagnetic metal/ferrimagnetic insulator heterostructures

Spin-Hall nano-oscillators (SHNOs) are promising spintronic devices to realize current controlled GHz frequency signals in nanoscale devices for neuromorphic computing and creating Ising systems. However, traditional SHNOs devices based on transition metals have high auto-oscillation threshold currents as well as low quality factors and output powers. Here we demonstrate a new type of hybrid SHNO based on a permalloy (Py) ferromagnetic-metal nanowire and low-damping ferrimagnetic insulator, in the form of epitaxial lithium aluminum ferrite (LAFO) thin films. The superior characteristics of such SHNOs are associated with the excitation of larger spin-precession angles and volumes. We further find that the presence of the ferrimagnetic insulator enhances the auto-oscillation amplitude of spin-wave edge modes, consistent with our micromagnetic modeling. This hybrid SHNO expands spintronic applications, including providing new means of coupling multiple SHNOs for neuromorphic computing and advancing magnonics.

Spin-Hall nano-oscillators (SHNOs) are promising spintronic devices to realize current controlled GHz frequency signals in nanoscale devices for neuromorphic computing and creating Ising systems. However, traditional SHNOs devices based on transition metals have high auto-oscillation threshold currents as well as low quality factors and output powers. Here we demonstrate a new type of hybrid SHNO based on a permalloy (Py) ferromagnetic-metal nanowire and low-damping ferrimagnetic insulator, in the form of epitaxial lithium aluminum ferrite (LAFO) thin films. The superior characteristics of such SHNOs are associated with the excitation of larger spin-precession angles and volumes. We further find that the presence of the ferrimagnetic insulator enhances the auto-oscillation amplitude of spin-wave edge modes, consistent with our micromagnetic modeling. This hybrid SHNO expands spintronic applications, including providing new means of coupling multiple SHNOs for neuromorphic computing and advancing magnonics.
High-efficiency oscillators are essential to accelerate the application of spintronics for neuromorphic computing [1][2][3][4] , Ising systems 5 , and magnonic devices [6][7][8] , among other applications. Spin-Hall nano-oscillators (SHNOs) are one of the important approaches to achieve these applications due to their two-dimensional geometry, which permits coupling multiple SHNOs in a plane [9][10][11] , as well as their ease of fabrication. Several geometries of SHNOs have been proposed in previous studies, such as nanodisk [12][13][14] , nanowire [15][16][17] , and nanoconstriction types [18][19][20][21][22] . However, these SHNOs generally have high threshold currents, low emission powers, and poor quality factors because of the nature of their constituent materials, specifically the large magnetic damping in transition metal ferromagnets. In recent years, attention has focused on ferrimagnetic insulators [23][24][25][26] due to their extremely low damping and, consequently, high magnon conductivity 27 , which is very favorable for spintronic applications. At the same time, this low damping characteristic facilitates the formation of spin-Hall effect-induced auto-oscillations; indeed, ferrimagnetic insulator-based nano-oscillators have been demonstrated with yttrium iron garnet/Pt bilayers 25,26 . Nevertheless, they suffer from low power emission due to their small inverse spin-Hall effect signals 28 . Joule heating also limits their application at room temperature 28 . One way to overcome these drawbacks is by creating a new type of hybrid SHNOs based on ferromagnetic metal-ferrimagnetic insulator heterostructures. Interesting physics emerges when coupling thin layers of these two types of materials [29][30][31][32] . When the two layers are weakly coupled, there are two distinct spin resonances, associated with acoustic and optical modes. However, when they are strongly coupled, the two layers act collectively, leading to magnetic properties inherited from both layers 33 , specifically a lower effective damping. Thus, SHNOs fabricated from such heterostructures can take advantage of the low damping from the ferrimagnetic insulator layer and yet maintain a strong electrical signal from the ferromagnetic metal layer.
Theoretical studies have shown that a uniform spin current applied to an extended magnetic thin film does not support the formation of auto-oscillations due to the emergence of nonlinear damping from magnon-magnon interactions 34 . However, by concentrating spin current in a small region, linear spin-wave mode autooscillation states can be stabilized 35 . Later, it was shown that nonlinear localized modes 36 could also be achieved due to the suppression of magnon-magnon interactions, which has been experimentally demonstrated in point-contact type and disk-type SHNOs [12][13][14]37 . Meanwhile, if the device geometry is confined (e.g., a nanowire or nanoconstriction), auto-oscillations can still be excited in a localized region that leads to a potential well that limits spin-wave propagation 16,20 . These self-localized modes can have much smaller threshold currents than linear modes due to lower radiative loss in an auto-oscillation state.
In this article, we demonstrate a new type of SHNO that combines ferromagnetic transition metals Ni 80 Fe 20 (Py) with an epitaxial thin film ferrimagnetic insulator, lithium aluminum ferrite (LAFO). This hybrid SHNO expands spintronic applications, including providing new means of coupling multiple SHNOs for neuromorphic computing and can advance designs for magnonics. Furthermore, compared to conventional Py/Pt SHNOs, this hybrid SHNO is superior in all important characteristics, having a reduced threshold current, stronger emission power, and higher quality factor.
To determine the magnetic properties in different Py/LAFO samples, ferromagnetic resonance spectroscopy (FMR) measurements were carried out on unpatterned thin films and heterostructures via a vector network analyzer (VNA) technique 38 . Effective magnetization M eff and anisotropy field H a are obtained by fitting resonance peaks to the Kittel model f = μ 0 γ=2π ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðH + H a ÞðH + H a + M eff Þ p , where H is the external magnetic field, M eff is the effective magnetization, γ is the gyromagnetic ratio, and μ 0 is the vacuum permeability. Both LAFO and LFO have magnetocrystalline anisotropy with an easy axis along <110> and a hard axis along <100> directions that is characterized by an inplane anisotropy field H a . Gilbert damping constants α are obtained by measuring and fitting the FMR linewidth as a function of the frequency. The data and fits are shown in Fig. 1b, c and the fitting parameters are listed in Supplementary Table S1. There was always only one FMR absorption peak observable, indicating that the two magnetic layers in our Py/LAFO heterostructures are strongly coupled. Further, the M eff of Pt/Py/LAFO falls between the M eff of bare LAFO or LFO and Py layers, as expected for two ferromagnetically coupled magnetic layers. To analyze the change of M eff and α in the heterostructures, a macrospin model based on Landau-Lifshitz-Gilbert (LLG) equation considering two strongly coupled magnetic layers is used (see Supplementary Note 7). When two magnetic layers are strongly ferromagnetic coupled, the acoustic mode resonance condition will be set by the  Supplementary Table S1 and are compared to the model's M eff and α. M eff obtained from the simple model is always smaller than the actual measured value, while α is always larger than the measured value, which indicates that the exchange coupling is smaller than that of the weighted mean of the two layers. As the damping of the coupled magnetic layers decreases, a spin current injected into the Py layer in LAFO/Py/Pt heterostructures can excite a larger magnetic volume, which, as we show, greatly improves device performance.
To compare the magnetic excitations of thin films with patterned structures, we conducted spin-torque FMR (ST-FMR) on both 2 µm wide stripe devices and 400 nm wide nanowire devices. Figure 2a, b show the ST-FMR spectra of 400 nm wide nanowire devices. In contrast to the FMR spectra, ST-FMR shows two dominant resonances, whose linewidth and peak amplitude are sensitive to bias current. While for 2 µm width stripe devices, only one ST-FMR peak is seen ( Supplementary Fig. S2a). Figure 2c shows the ST-FMR frequency-resonance field spectra of a 400 nm nanowire and a 2 µm stripe LAFO20/Py5/Pt5 device. We find that the dispersion of the higher frequency mode of the two devices overlap, with a fit to the Kittel model giving μ 0 M eff = 0.86 T, close to that found from the FMR spectra of the associated unpatterned film. We thus attribute this feature to a bulk mode (BM), a spin excitation that is most uniform across the width of the device. The lower frequency mode only appears in the 400 nm wide device and is associated with a much lower μ 0 M eff = 0.65 T. We attribute this lower frequency mode to an edge mode (EM), as indicated in Fig. 2a, b, and this conclusion is supported by micromagnetic simulations, as discussed below. Two modes of this type have been reported in previous studies [15][16][17]20 .
Hybrid SHNO devices show the onset of auto-oscillations at a threshold current. Figure 2d-g shows the power spectral density (PSD) as a function of bias current at fixed field H = 0.0817 T for ϕ = 70 o . In all the devices, the auto-oscillation frequency redshifts with increasing bias current, a characteristic of localized modes in nanowire SHNOs 16,17 . This is not a pure heating effect (see Supplementary Fig. S4). Interestingly, the threshold current I th drops dramatically between the reference sample, Py5/Pt5, and the sample with LAFO, LAFO4/Py5/Pt5, and then the I th slowly increases with the thickness of LAFO. The slow increase of I th with the thickness of the LAFO layer agrees well with the prediction of the macrospin model   Fig. S2b, c). However, the drop of I th from Py5/Pt5 to LAFO4/Py5/Pt5 cannot be explained by this model. We note this decrease in I th is observed in ST-FMR studies conducted on both 400 nm nanowire and 2 µm width strip samples, showing that it does not depend sensitively on sample geometry. It is thus possible that the spin current generated from the Py layer itself acts on the LAFO to increase the spin torques and reduce I th [39][40][41][42] ; previous studies have experimentally shown that spin-orbit torque can be generated from a single magnetic layer 19,43 . In addition, the edge mode can be dominant in hybrid devices and cause a moderelated change of nonlinear damping 44,45 , which would reduce radiative loss and thus reduce I th . Nevertheless, further study is required to explain this drop of I th .
Notice that compared to the Py5/Pt5 sample, the slopes of the redshift increase in all LAFO samples. This is likely due to larger spinprecession angles and the emergence of a nonlinear self-localized mode 18 . Interestingly, the relative magnitude of EM and BM measured from ST-FMRs and PSDs both follow the same trend: the dominant mode transitions from a BM in Py5/Pt5 to an EM in LAFO20/Py5/Pt5, which simultaneously increases the performance of the oscillators. This transition will be discussed in detail in the next section. Threshold currents and auto-oscillation currents extrapolated from the ST-FMR data and determined directly from PSD for different devices are listed in Supplementary Table S2.
To investigate the spin-wave modes of Py and Py/LAFO SHNO heterostructures, micromagnetic simulations were carried out using MuMax3 (see Methods) 46 . Spin currents were applied solely to the 400 nm Py nanowire's central region to mimic the device's current distribution. The simulation is run until a steady state response is observed. The time evolution of magnetization was then converted to the frequency domain by Fast Fourier transform (FFT). Figure 3a shows the spatial-averaged FFT amplitude in the center region of Py for different samples, confirming the experimental observation of two dominant auto-oscillation modes. From these simulations, we can find that the auto-oscillation frequencies and their trends are in excellent agreement with our experimental results: (i) the resonance frequency is almost not changed from the Py5/Pt5 device to the LAFO4/Py5/Pt5 device, then increases with the thickness of LAFO. This is mainly due to variations in the net M eff , as the resonance frequency strongly depends on M eff ; this shift of resonance frequency closely follows the trends in M eff determined by FMR and ST-FMR measurements, as shown in Supplementary Table S1; (ii) the high-frequency mode has a higher amplitude in Py5/Pt5, while the low-frequency mode gradually becomes dominant with increasing LAFO thickness; (iii) the peak amplitude and quality factor for LAFO20/Py5/Pt5 is significantly higher than that of Py5/Pt5. To identify the reason behind this transition, pixel-wise spatial FFTs were conducted on Py5/Pt5 and LAFO20/Py5/ Pt5 simulations. Spatial FFT images of the Py layer from Py5/Pt5 at the auto-oscillation frequencies are shown in Fig. 3b. We find that the lowfrequency peak at f = 6.21 GHz is concentrated on the edges of the Py stripe, while the peak at f = 7.17 GHz is dominant in the middle. This observation is consistent with our assignment of the modes in the previous section and earlier studies 15,16 .
More interesting magnetic behavior occurs in the simulation of hybrid SHNO devices. Spatial FFT images of Py and LAFO layers from the LAFO20/Py5/Pt5 simulation are shown in Fig. 3c. Compared to Py5/ Pt5, the EM and BM of the Py layer excited in LAFO20/Py5/Pt5 shows a much larger oscillation amplitude. The magnetization of the LAFO layer oscillates coherently with that of the Py layer. The increased autooscillation amplitude is mainly due to a larger precession cone angle in the Py layer, caused by the lower effective damping constant. Meanwhile, the area of the EM expands in the bilayer system, which leads to a larger excited volume of moments, consistent with a higher quality factor. The out-of-plane expansion of both BM and EM is caused by the strong ferromagnetic coupling between the two layers, while the inplane expansion of EM can be understood in this way: the exchange field generated by the LAFO layer tends to align the moments at the edge of Py nanowires against the demagnetization field, which decreases the effective field inhomogeneity, thus increasing the EM coherent oscillation volume. This is confirmed by plotting the transverse magnetization profile of the devices at equilibrium (Supplementary Fig. S3a), where one can observe a smoother transition near the edge of Py layer in the LAFO20/Py5/Pt5 device. This expands the area of the localized mode, especially the EM, greatly enhancing the coherence of each mode and thus increasing the maximum power and quality factor of signals emitted from the oscillators. To better understand the properties of the auto-oscillation modes, maps of the PSD as a function of the magnetic field at a fixed bias current (1.15 times I th ) are plotted in Fig. 4a-d. Similar to the current dependent PSD map (Fig. 2d-g), BM and EM are observed. By fitting the two PSD peaks to Lorentzian functions, we can obtain the auto-oscillation frequencies and dispersion curves for the BM and EM as shown in Fig. 4e-h. This is shown in comparison to the FMR and ST-FMR results. In the Py5/Pt5 sample (Fig. 4a), only the BM is detectable, and its dispersion curve is slightly redshifted compared to that of FMR and ST-FMR data. However, contrary to the commonly seen selflocalized mode 13,36 in magnetic thin films, in a magnetic wire, the propagation of spin waves is restricted in the transverse direction but allowed along the wire direction, preventing mode localization. This BM has a similar I th compared to the uniform mode 35 , which is confirmed by the ST-FMR on 2 µm stripes ( Supplementary Fig. S2b). Instead, the EM is localized due to a self-induced potential well, leading to a localized quasi-linear auto-oscillation mode.
In LAFO/Py/Pt hybrid samples (Fig. 4b-d), due to the strong coupling between two magnetic layers, the center region of LAFO will precess coherently with Py. The exchange fields generated from the  LAFO layer change the auto-oscillations frequencies in LAFO/Py/Pt samples. The increased difference between the dispersion curves of auto-oscillation and those obtained from FMR and ST-FMR supports the idea that the spin-wave modes are more localized in the LAFOcontaining devices. As shown in Fig. 4e-h, compared to the Py5/ Pt5 sample, the dispersion curve of the BM of the LAFO4/Py5/ Pt5 sample from PSD measurements is much lower than the FMR mode. This is one of the key characteristics of a mode that is more strongly localized. According to the discussion in the previous sections, we determined a few critical properties of the ferrimagnetic insulator layer which can guide us to design a better hybrid SHNOs: (i) low α ferrimagnetic insulator to have lower α, (ii) higher M eff to make the autooscillation EM more localized and (iii) appropriate thickness to not increase the threshold current. To meet these criteria, LFO (15 nm), which contains a higher Fe concentration compared to LAFO, possesses these critical properties (as listed in Supplementary  Table S1) and was used in place of LAFO as the ferrimagnetic insulator in our designed device. As shown in Fig. 5a, b, strong auto-oscillation signals up to 30 dB over the noise floor (NF) are detected, associated with EMs. Compared to the LAFO samples, the auto-oscillations occur at a higher frequency due to the larger M eff of the LFO layer. Figure 3c is the dispersion curves obtained from FMR, ST-FMR, and PSD measurements for LFO15/Py5/Pt5 sample. Since FMR spectra are measured at ϕ = 0 o (magnetic hard axis) and the ST-FMR spectra are measured at ϕ = 70 o (closer to the magnetic easy axis direction), a significant difference between these results occurs due to the large in-plane crystalline anisotropy of the LFO layer. The strong anisotropy also causes a crossing between the maximum PSD signal and ST-FMR curves at low fields in Fig. 5c. At this low field region, the sample is not magnetically saturated as we are not measuring the PSD with the field along the easy axis of LFO. This leads to multidomain states at low field and a resonance frequency that does not dependent monotonically on the applied field. However, at a higher field, the PSD dispersion curve is closer to what we obtained from ST-FMR. The auto-oscillation dispersion in this field range is redshifted relative to ST-FMR dispersion, which again indicates the formation of localized auto-oscillation modes. To systematically compare the performance of different samples, PSDs at a fixed field H = 0.045 T obtained from the fielddependent PSD maps are plotted in Fig. 5d. Clearly, with the optimization of the ferrimagnetic insulator layer, the maximum power in hybrid samples can be at least a 1000 times larger than that of the Py5/Pt5 sample. We note that the anisotropic magnetoresistance (AMR) does not vary significantly in the different samples (see Supplementary Fig. S1) and is thus not an important factor in the change of device output power. By fitting the dominant peak of the PSDs with a Lorentzian function, we obtained both the maximum power and maximum quality factor from each device, as shown in Fig. 5e. From all these results, compared to the conventional Py/Pt SHNOs, we can obtain orders of magnitude higher emission power and quality factor in the hybrid SHNOs. In addition, the feasibility of generating and transporting spin waves in the low damping insulator layer provides a new platform for applications of SHNOs.
In summary, our work presents a new hybrid type of SHNOs, which shows superior performance compared to conventional Py/Pt spin oscillators. In hybrid SHNOs, much higher power emission and quality factors can be obtained relative to conventional Py/Pt SHNOs. To understand the mechanism behind the improved performance, ferromagnetic resonance measurements, and micromagnetic simulations were carried out on both conventional Py/Pt SHNO and hybrid SHNOs. Results show that the two magnetic layers precess coherently in bulk and edge modes. Meanwhile, the localization of autooscillations reduces the threshold current and makes the edge mode the dominant power emission source rather than the bulk mode. Further, by designing the composition and thickness of the ferrimagnetic insulator layer, we successfully fabricated hybrid SHNOs with better performance by replacing LAFO with LFO. Our work expands the possibility of SHNOs for many types of spintronic applications,  47,48 . After the growth of the ferrite thin films of various thicknesses and compositions, Py(5 nm)/Pt(5 nm) bilayers are deposited on LAFO and LFO via a Kurt Lester magnetron sputtering system at room temperature. The reference sample Py5/Pt5 is deposited on a c-sapphire (0001) substrate. The as-deposited samples are then spin-coated with PMMA 495 4A and exposed by an Elionix 50 keV E-beam lithography system for the nanowires' patterning. After the development process, the samples are transferred to the Kurt Lester system for Ar plasma dry etching. Residual resists were removed in a ultrasonic cleaner before waveguides with 400 nm gaps between two contact pads are created by E-beam lithography. Finally, Cr(5 nm)/Au(50 nm) contacts are deposited. Experimental techniques. VNA-FMR is used for detecting the thin film samples' ferromagnetic resonance. For pure LAFO samples, a field-modulated technique is used to detect the low linewidth resonance peaks. The samples are always mounted with the dc magnetic field applied along the in-plane [100] hard axis (φ = 0°) of the LAFO thin film. ST-FMR measurements are carried out in a probe station with the external field always applied at φ = 70°with respect to the current direction. The field is modulated with a coil and the signal is detected by a lock-in amplifier. The DC bias is applied via a Keithley 2400. PSDs are measured via Keysight N9030B spectrum analyzer with a noise floor extension option. Input signals are amplified by an internal 29 dB low-noise amplifier. During the measurement, the resolution bandwidth is always kept at 1 MHz. The noise floor in this setup is −125 dBm. To exclude sample-to-sample variations of resistances, ST-FMRs, and PSD maps, additional samples with the same geometry and composition are measured and shown in Supplementary Note 6.
Micromagnetic simulations. Micromagnetic simulations are run by the Mumax3 micromagnetic simulator 46 . The mesh size is set to 300 × 300 × 5, and each cell size is 5 × 5 × 5 nm 3 . This length is smaller than the exchange length of Py and LAFO. The top Py layer is designed as a stripe in the center with dimension 400 × 1500 × 5 nm 3 , while the bottom LAFO layer is extended to the boundaries and varied in thickness. Periodic boundary conditions along the long axis of the Py nanowire are used to eliminate the demagnetization field from the end of the Py stripe. The exchange constant between the Py and LAFO layers is taken to be half of the harmonic mean of the two layers. To reduce the spin-wave reflection at the boundary, we set an exponentially increased damping region near the boundaries of the simulated region. The applied spin current is restricted to the center region of the Py nanowire with dimension 500 × 400 × 5 nm 3 , since most of the spin current is concentrated between the two Au contacts. Threshold currents are found by running simulations over 200 ns and slowly increasing the applied current until m z starts to converge to a stable auto-oscillation state. In order to determine the auto-oscillation spectrum in the frequency domain, we set the current to be 1.2 times the threshold current found above and run the simulation for 500 ns. We use FFT algorithms to convert the magnetization evolution in the time-domain to the frequency domain. This method can be used to generate the auto-oscillation spectrum of the full device using the spatial-averaged m z ðtÞ or to generate the spatial profile of each autooscillation modes from m z ðr, tÞ. Simulation details for different samples are summarized in Supplementary Note 4, and used parameters are listed in Supplementary Table S3.

Data availability
The datasets generated during and/or analyzed during the current study are available in Supplementary Materials and also available from the corresponding authors on reasonable request.